That is why, you should define a graph of a function as a locus, coordinates of points of which M (x, y) are tied by the given functional dependence.Ĭopyright © 2002-2007 Dr. It’s possible, that intermediate points, not plotted on a graph, lie far from the drawing smooth curve. Such graphical representation of a function permits to visualize a behavior of the function, but has an insufficient attainableĪccuracy. , F by a smooth curve, we receive a graph of the given As a result a set of pointsģ) Joining marked points A, B, C. Marking according to the selected scale a set of x-coordinates on x-axis and a set of To represent a functional dependence y = f ( x ) as a graph it is necessary:ġ) to write a set of values of the function and its argument in a table:Ģ) To transfer the coordinates of the function points from the table to a coordinate system, So,įor each point on a plane a pair of numbers (x, y) corresponds, and inversely, for each pair of real numbers (x, y) the See: a point M has an abscissa x = 2, an ordinate y = 3 a point K has an abscissa x = Figure 1: Some basic elements of a graph (a) The horizontal axis is called the abscissa and the vertical axis is called the ordinate. Other examples come later in Figures 5, 6, and 7. Figure 1 shows some basic elements of a graph. Usually positive abscissasĪre placed by right on an axis XX’ positive ordinates – by upwards on an axis YY’. 1.1 Basic layout of a graph Certain conventions are used when plotting graphs. the portion of a given line intercepted between a fixed point within it, and an ordinate drawn to it from a given point without it. They are considered as positive or negative according to the adopted positive and negative directions of coordinate axes. Literally, a line or distance cut off spec. Values x = OP and y = OQ are called Cartesian coordinates ( or simply – coordinates ) of a point M. Number y, measuring its length - an ordinate or y-coordinate of a point M. The line need not actually go through each data point. Is called an abscissa or x-coordinate of a point M the segment OQ on axis YY’ and a Transcribed image text: GRAPHS 1) Graph 1: plot t on the abscissa versus y on the ordinate and artistically) draw a smooth line through the points. The segment OP on the axis XX’ and a number x, measuring its length according to the selected scale, An arbitrary scale is selected on each axis of coordinates.įind projections P and Q of a point M to the coordinate axes XX’Īnd YY’. The point O of their intersection isĬalled an origin of coordinates. For a set of points having the same ordinate and different abscissa, the line joining. ![]() The axis XX’ is called an x-axis, the axis YY’ – an y-axis. The ordinate gives the horizontal distance of a point from the origin. Straight lines XX’ and YY’ are called axes ofĬoordinates. Two mutually perpendicular straight lines XX’ and YY’ ( Fig.1 ) formĪ coordinate system, called Cartesian coordinates. Cartesian coordinates.Īxes of coordinates. Graphical representation of functionsĬoordinates.
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